Programming an algebraic experiment
- To: mathgroup at smc.vnet.net
- Subject: [mg34687] Programming an algebraic experiment
- From: riefler at iwt.uni-bremen.de
- Date: Sat, 1 Jun 2002 04:28:47 -0400 (EDT)
- Organization: Universitaet Bremen, Germany
- Sender: owner-wri-mathgroup at wolfram.com
Hi Given 4 complex numbers S1, S2, S3 and S4 with Si = xi + i*yi, i=1,2,3,4. These 4 numbers are the basis for the following 16 eqn.s: S11 = 1/2 * ( abs(S1)^2 + abs(S2)^2 + abs(S3)^2 + abs(S4)^2 ); S12 = 1/2 * ( - abs(S1)^2 + abs(S2)^2 - abs(S3)^2 + abs(S4)^2 ); S13 = real( S2*conj(S3) + S1*conj(S4) ); S14 = imag( S2*conj(S3) - S1*conj(S4) ); S21 = 1/2 * ( - abs(S1)^2 + abs(S2)^2 + abs(S3)^2 - abs(S4)^2 ); S22 = 1/2 * ( abs(S1)^2 + abs(S2)^2 - abs(S3)^2 - abs(S4)^2 ); S23 = real( S2*conj(S3) - S1*conj(S4) ); S24 = imag( S2*conj(S3) + S1*conj(S4) ); S31 = real( S2*conj(S4) + S1*conj(S3) ); S32 = imag( S2*conj(S4) - S1*conj(S3) ); S33 = real( S1*conj(S2) + S3*conj(S4) ); S34 = imag( conj(S1)*S2 + conj(S3)*S4 ); S41 = imag( conj(S2)*S4 + S1*conj(S3) ); S42 = imag( conj(S2)*S4 - S1*conj(S3) ); S43 = imag( S1*conj(S2) - S3*conj(S4) ); S44 = real( S1*conj(S2) - S3*conj(S4) ); "abs" stands for the absolute value and "conj" for the complex conjugate value of the Si. Now my aim is to find any combination - independent how long - with and between these Sii to get the following result: K=y1+y2 Now my question to you is: How can I instruct Mathematica that it will look for an answer? I want to see Mathematica that it is carried out as much as possible combinations, simplify these combinations algeabraically and then compare the simplified solution with K. Thank you Norbert